Finite Group Databasebeta

← #14816901

Subgroups — #14816901

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13071527C211yesmaximal, characteristic, complemented
4#13070137C211yesmaximal, characteristic, complemented
5#13070097C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069941C211yesmaximal, characteristic, complemented
8#13069341C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic
11#13068967C211yesmaximal, characteristic
12#13068877C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic, complemented
15C11×#2452C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#396—21no—
24C11×#393—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#385—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622697—24no—
35C4×#4323—24no—
36#10622602—21no—
37#10622602—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622280—21no—
52D11×#95—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—41no—
70C11×C22⋊Q8—44no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4323—22no—
90C2×#4323—22no—
91C2×#4323Q814yescomplemented
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C4×D44—22no—
105C4×D44—22no—
106C4×D44—22no—
107C4×D44—22no—
108C4×D44—41no—
109C4×D44—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#66896—22no—
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66873—22no—
122#66873—22no—
123#66873D414yes—
124#66872—22no—
125#66872—22no—
126#66872—22no—
127#66871—22no—
128#66871—41no—
129C4⋊(C11⋊C8)—22no—
130C4×C11⋊C8—22no—
131#26380—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11—21no—
134C2×Q8×C11—42no—
135C2×Q8×C11—42no—
136C2×Q8×C11—81no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×Q812yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44C2×D412yes—
163C2×D44C2×Q812yes—
164C2×D44#4112yes—
165C2×C4×D11—24no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—81no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4C2×D412yes—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—81no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196#4323—28no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—81no—
207Dic11⋊C4—81no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8C2×Q812yes—
220C2×#476—111no—
221C2×C4×D8—111no—
222#2452D1111yescharacteristic, complemented
223#2349—111no—
224#2092—111no—
225#2085—111no—
226#2065—111no—
227#2057—111no—
228#1941—111no—
229#1916—111no—
230#1879—111no—
231#1879—111no—
232#1864—111no—
233#1864—111no—
234#1862—111no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250Q8×C11—84no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—41no—
254D4×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—84no—
281C2×C4×C11#13512yes—
282C2×C4×C11AGL(1,ℤ/8)12yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×Q811yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C2×Dic11—22no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298D44—22no—
299D44—22no—
300D44—22no—
301D44C22⋊Q814yescomplemented
302C4×D11—84no—
303C4×D11—84no—
304C4×D11—84no—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C22×D8—111no—
310C2×C4⋊Q8C2×D1111yescharacteristic
311C2×C22⋊Q8—21no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—111no—
315C2×C4×D4C2×D1111yescharacteristic
316#476—224no—
317C4×D8—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×C4×C8—111no—
331#396—21no—
332#393—21no—
333#390C2×D1111yescharacteristic
334#390C2×D1111yescharacteristic
335#389—111no—
336#389—111no—
337#389C2×D1111yescharacteristic
338#389C2×D1111yescharacteristic
339#385—21no—
340#385—221no—
341#385—221no—
342#382—111no—
343#380—221no—
344C4×C4⋊C4C2×D1111yescharacteristic
345C2×#95—221no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#336—111no—
351#336—111no—
352#336—111no—
353#336—111no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11#52511yescharacteristic
362C22×C11D4211yescharacteristic
363C22×C11D4×Q811yescharacteristic
364C22×C11C2×#13511yescharacteristic
365C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57711yescharacteristic
368C2×D11—24no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—42no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×C22⋊Q811yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54711yescharacteristic
387C4×C11#55411yescharacteristic
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—21no—
392C22×D4—111no—
393C22×D4C22×D1111yescharacteristic
394C23×C4—21no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C2×D8—114no—
399C2×D8—222no—
400C2×D8—222no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—111no—
405C4⋊Q8—22no—
406C4⋊Q8—41no—
407C22⋊Q8—44no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—441no—
415C4×D4—441no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22⋊D1111yescharacteristic
425C2×C4⋊C4C22⋊D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439C2×C42C22×D1111yescharacteristic
440#107—222no—
441#107—441no—
442#106—222no—
443#106—222no—
444#106—222no—
445C4⋊C8—222no—
446#102—114no—
447#102—222no—
448#102—222no—
449#102—222no—
450#102—222no—
451#102—441no—
452C4×C8—222no—
453#95—21no—
454#95—21no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95C22⋊D1111yescharacteristic
460#95C22⋊D1111yescharacteristic
461C2×C11—82no—
462C2×C11#244911yescharacteristic
463C2×C11#310611yescharacteristic
464C2×C11#311811yescharacteristic
465C2×C11#326411yescharacteristic
466C2×C11#328211yescharacteristic
467C2×C11#338011yescharacteristic
468C2×C11#338411yescharacteristic
469D11—44no—
470C24—21no—
471C24—221no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—112no—
481C2×D4—112no—
482C2×D4—112no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4Q8×D1112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—224no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4—881no—
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512D8—228no—
513C2×C8—112no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—112no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—881no—
542C4⋊C4—881no—
543C4⋊C4D4×D1112yes—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—224no—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C11#2638011yescharacteristic, complemented, Sylow
559C23—22no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—222no—
567C23—222no—
568C23—222no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23C22×C22⋊D1111yescharacteristic
574Q8—84no—
575D4—22no—
576D4—22no—
577D4—41no—
578D4—41no—
579D4—114no—
580D4—222no—
581D4—222no—
582D4—222no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—84no—
609C2×C4—222no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4—884no—
620C2×C4—884no—
621C2×C4#6698512yes—
622C2×C4#6700312yes—
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4C2×Q8×D1111yescharacteristic
626C2×C4#6704011yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C8—222no—
630C8—222no—
631C8—441no—
632C8—441no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—224no—
641C22—442no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22—442no—
646C22—442no—
647C22C2×#6698511yescharacteristic
648C22D4×C22⋊D1111yescharacteristic
649C22Q8×C22⋊D1111yescharacteristic
650C22C2×#6700311yescharacteristic
651C22#1062335911yescharacteristic
652C22#1062336611yescharacteristic
653C22#1062336811yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—81no—
662C4—81no—
663C4—442no—
664C4—881no—
665C4—881no—
666C4D11×C22⋊Q811yescharacteristic
667C4#1062316211yescharacteristic
668C4#1062316711yescharacteristic
669C4#1062316911yescharacteristic
670C2—82no—
671C2—444no—
672C2#1307242211yescharacteristic
673C2#1307867011yescharacteristic
674C2#1307879411yescharacteristic
675C2#1308009211yescharacteristic
676C2#1308032411yescharacteristic
677C2#1308147911yescharacteristic
678C2#1308151111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2452C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2452D11
hypocenterC11#26380
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13071527C2semidirect
4. #13070137C2semidirect
5. #13070097C2semidirect
6. #13069990C2semidirect
7. #13069941C2semidirect
8. #13069341C2semidirect
9. #13069175C2semidirect
12. #13068877C2semidirect
13. #13068876C2semidirect
14. #13068862C2semidirect
15. C11×#2452C2semidirect
91. C2×#4323Q8semidirect
222. #2452D11semidirect
301. D44C22⋊Q8semidirect
558. C11#26380semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226972
C2×C4×#43232
#130715272
#130701372
#130700972
#130699902
#130699412
#130693412
#130691752
#130689672
#130688772
#130688762
#130688622
C11×#24522
#2638011